NEET Chemical Kinetics — Set 13

Question 1

A first-order gaseous reaction has an initial pressure of 2.4 atm. After 40 s, the total pressure is 3.0 atm. What is the rate constant?

Accepted Answer

For $ \text{A} \to \text{B} + \text{C} $, $ p_t = p_i + x $, $ x = 3.0 - 2.4 = 0.6 \, \text{atm} $. $ p_A = p_i - x = 2.4 - 0.6 = 1.8 \, \text{atm} $. $ k = \frac{2.303}{40} \log \frac{2.4}{1.8} = \frac{2.303 \times 0.125}{40} \approx 0.0072 \, \text{s}^{-1} $.

Question 2

A first-order reaction has an initial concentration of $ 0.5 \, \text{mol L}^{-1} $ and a rate constant of $ 0.0693 \, \text{min}^{-1} $. What is the concentration after 20 minutes?

Accepted Answer

For first-order, $ \log \frac{[\text{R}]_0}{[\text{R}]} = \frac{k t}{2.303} $. $ \log \frac{0.5}{[\text{R}]} = \frac{0.0693 \times 20}{2.303} \approx 0.602 $, $ \frac{0.5}{[\text{R}]} = 10^{0.602} \approx 4 $. $ [\text{R}] = \frac{0.5}{4} = 0.125 \, \text{mol L}^{-1} $.

Question 3

A second-order reaction has a rate constant of $ 0.03 \, \text{L mol}^{-1} \text{min}^{-1} $ and an initial concentration of $ 0.15 \, \text{mol L}^{-1} $. What is the half-life?

Accepted Answer

For second-order, $ t_{1/2} = \frac{1}{k [\text{A}]_0} $. Given: $ k = 0.03 \, \text{L mol}^{-1} \text{min}^{-1} $, $ [\text{A}]_0 = 0.15 \, \text{mol L}^{-1} $. $ t_{1/2} = \frac{1}{0.03 \times 0.15} = \frac{1}{0.0045} \approx 222.22 \, \text{min} $.

NEET Chemistry: Chemical Kinetics — Practice Set 13

Q1. A first-order gaseous reaction has an initial pressure of 2.4 atm. After 40 s, the total pressure is 3.0 atm. What is the rate constant?

Q2. A first-order reaction has an initial concentration of \( 0.5 \, \text{mol L}^{-1} \) and a rate constant of \( 0.0693 \, \text{min}^{-1} \). What is the concentration after 20 minutes?

Q3. A second-order reaction has a rate constant of \( 0.03 \, \text{L mol}^{-1} \text{min}^{-1} \) and an initial concentration of \( 0.15 \, \text{mol L}^{-1} \). What is the half-life?

Q4. The rate constant of a reaction increases from \( 2.0 \times 10^{-3} \, \text{s}^{-1} \) at 320 K to \( 8.0 \times 10^{-3} \, \text{s}^{-1} \) at 340 K. What is the activation energy (\( R = 8.314 \, \text{J mol}^{-1} \text{K}^{-1} \))?

Q5. A zero-order reaction has an initial concentration of \( 0.24 \, \text{mol L}^{-1} \) and a rate constant of \( 3.0 \times 10^{-3} \, \text{mol L}^{-1} \text{s}^{-1} \). What is the half-life?

Q6. A first-order reaction has a rate constant of \( 0.0346 \, \text{min}^{-1} \). What is the half-life?

Q7. For the reaction \( \text{A} + 2\text{B} \to 3\text{C} \), the rate of formation of C is \( 0.15 \, \text{mol L}^{-1} \text{s}^{-1} \). What is the rate of disappearance of B?

Q8. A reaction has the rate law \( \text{Rate} = k[\text{A}]^{1/3}[\text{B}]^{2/3} \). What is the overall order?

Q9. The rate of a reaction is \( \text{Rate} = k[\text{A}]^{0.5}[\text{B}]^{0.5} \). What is the overall order?

Q10. A second-order reaction has a rate constant of \( 0.06 \, \text{L mol}^{-1} \text{s}^{-1} \). If the initial concentration is \( 0.2 \, \text{mol L}^{-1} \), what is the time for 60% completion?